The resistor is one of the most common elements in an electrical circuit. With its help, the current is limited and the voltage changes. When designing circuits, it is often necessary to calculate the resistance to step down the voltage. This is important when building dividers for digital devices or power supplies, so every radio amateur should be able to perform such calculations.
Content
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Physical definition
- Resistance value
- Resistor impedance
- Parallel connection
- Sequential inclusion
- Voltage divider calculation
- Calculations online
Physical definition
A resistor is an element that is used in an electrical circuit and does not require a power source for its operation. It is designed to transform current into voltage and vice versa. In addition, it can convert electrical energy into heat and limit the amount of current. But before calculating the voltage drop across the resistor, it is advisable to understand the essence of this process.
A resistor is a very common element, characterized by a number of parameters. The main ones are:
- resistance;
- the amount of dissipated energy;
- operating voltage;
- power;
- resistance to environmental influences;
- parasitic component.
A passive electrical element is indicated in the diagram as a rectangle with two leads from the middle of its lateral sides. In the center of the figure, the power can be indicated in Roman numerals or dashes. For example, the vertical bar represents the cell's withstand power of 1 Watt. The crossed out rectangle in the designations on the diagram indicates that such a resistor is variable.
Resistors can be produced with constant and variable resistance. A variety of the latter are trimmers. They differ from variables only in the way of setting the desired value.
On the diagrams and in the technical literature, the device is designated by the Latin letter R, next to which the serial number and its denomination are indicated in accordance with the International System of Units (SI). For example, R12 5kΩ is a 5kΩ resistor located in the circuit at number 12.
In the manufacture of the element, a resistive layer is used, which can be film or bulk. It is applied to a dielectric base and covered with a protective film on top.
Resistance value
Resistance is a fundamental quantity in electrical processes. Its value is invariably related to current and voltage. Their general dependence is described using Ohm's law: the current strength arising in the circuit section is directly proportional to the potential difference between the extreme points of this section and inversely proportional to its resistance. Resistance is found from this law according to the following formula:
R = U / I, where:
- R - resistance in the section of the circuit, Ohm.
- I is the current flowing through this section, A.
- U is the potential difference at the nodes of a part of the circuit, V.
In fact, the resistance of an element is determined by its physical structure and is due to the vibrations of atoms in the crystal lattice. Therefore, all materials differ into conductors, semiconductors and dielectrics, depending on the ability to conduct electricity.
Current is the directed movement of charge carriers. For its occurrence, it is necessary that the substance has free electrons. If an electric field is applied to such a physical body, then the charges it moves will begin to collide with structural inhomogeneities. These defects are formed due to various impurities, violation of the lattice periodicity, and thermal fluctuations. Striking them, the electron consumes energy, which is converted into heat. As a result, the charge loses momentum, and the magnitude of the potential difference decreases.
But Ohm's law is not applicable to all substances. In electrolytes, dielectrics and semiconductors, a linear relationship between the three quantities is not always observed. The resistance of such substances depends on the physical parameters of the conductor, namely, its length and cross-sectional area, while it is sensitive to temperature changes.
This dependence is described using the formula R = p * l / S. That is, the resistance is directly proportional to the length and inversely proportional to the area of the conductor. The p value is called resistivity and is determined by the type of material. Its value is taken from the directory.
Resistor impedance
Ohm's Law applies to an ideal resistor with no parasitic resistance. The impedance (impedance) is determined based on the equivalent circuit. The exact calculation of the resistance to lower the voltage must be carried out using other formulas. The equivalent resistor circuit, in addition to active impedance, also contains capacitive and inductive resistance.
The first leads to a slow accumulation of charge, which dissipates when the direction of the current changes. The larger the parasitic capacitance, the longer it takes to charge. Accordingly, the faster the current changes its direction, the lower its capacitive resistance. The second is characterized by a magnetic field, whose appearance prevents the current from changing direction, therefore, the faster the current changes its motion, the greater the inductive resistance becomes.
The impedance is calculated using the formula: I = U / Z, where Z = (R2 + (Xc-Xl) 2) ½. Where:
- R - active value, R = p * l / s.
- Xc - capacitive quantity, Xc = 1 / w * C.
- Xl - inductive quantity, Xl = w * C.
- w is the cyclic frequency, w = 2πƒ.
Knowing the total resistance of the resistor, you can more accurately calculate the voltage drop in it. But to measure parasitic components, you will need to use highly specialized instruments. In conventional calculations, the resistance is calculated taking into account only its active value, and parasitic values are taken as negligible.
Parallel connection
In electrical circuits, both parallel and serial connection are used on the sections of the circuit. The first is a circuit in which each of its elements is connected to the other by both contacts, but there is no direct electrical connection between its own terminals. T. e. there are two points (electrical nodes) to which several resistors are connected.
With this inclusion, the current passing through the node begins to split, and a different value will flow through each element. The amount of current at each element will be directly proportional to the resistance of the resistor, so the total conductance in this section will increase, and its impedance will decrease.
The formula with which you can calculate the total conductivity looks like this: G = 1 / Rtotal = 1 / R1 + 1 / R2 +… + 1 / Rn, where n - denotes the serial number of the resistor in the circuit.
Transforming this formula, you get an expression of the form: R total = 1 / G = (R1 * R2 *… * Rn) / (R1 * R2 + R2 * Rn +… + R1 * Rn. Having analyzed it, it can be concluded that when connected in parallel, the impedance will always be less than the smallest value of the individual resistor.
With such a connection, the voltage between the nodes is simultaneously the total potential difference for the entire section and across each individual resistor. Therefore, if we calculate the voltage drop on one device, then it will be the same on any parallel connected element: U total = U 1 = U 2 =… = U n.
But the electric current passing through a separate element, based on Ohm's law, will be equal to: I Rn = U Rn / R n.
Sequential inclusion
This is the name of combining two or more resistors into one section of the chain, in which they are connected to each other only at one point. The impedance in series connection is defined as the sum of the resistances of each individual element: Rtotal = R1 + R2 +… + Rn.
Consequently, the current flowing through such a circuit will become less and less after passing through a series-connected resistor. The more elements there are in the chain, the more difficult it will be for him to go through all of them. Thus, its total value is defined as Itot = U / (R1 + R2 +… + Rn).
Therefore, it can be argued that in series connection there is only one path for current flow. The more the number of resistors in the line, the less current will be in this section.
The drop in the potential difference with this type of connection at each element will have its own value. It is determined by the formula URn = IRn * Rn, and the greater the impedance of the element, the more energy will be released in it.
Voltage divider calculation
A resistive voltage divider is a simple circuit for lowering voltage. It can consist of two or more elements. The simplest divider can be represented in the form of two sections of the chain, which are called shoulders. One of them, which is located between the positive point of the potential and the zero point, is the upper one, and the other, between the negative and minus one, is the lower one.
This circuit is used to reduce the voltage in both DC and AC circuits. The essence of the process is as follows.
- Voltage U is applied to the resistive circuit from the power supply.
- Current begins to flow through the resistors in the series section of the circuit formed by resistors R1 and R2.
- As a result, a certain amount of energy is released on each of them, i.e. voltage drop occurs.
The sum of the voltages across the entire swing of the line is equal to the value of the potential difference of the power source. In accordance with the formula: U = I * R, the voltage drop is directly proportional to the current strength and the resistance value. Considering that the current flowing through the resistors is the same, the formulas U1 = I * R1 and U2 = I * R2 will be valid.
Then the total voltage drop in the section will be equal to U = I * (R1 + R2). Based on this, you can find the current strength: I = U / (R1 + R2). Using these two expressions, the final formulas for calculating the voltage drop across each element can be obtained:
- U1 = R1 * U / (R1 + R2);
- U2 = R2 * U / (R1 + R2).
The practical application of such a divider is very common due to the simplicity of the implementation of voltage reduction. For example, suppose the power supply outputs 12 V, and the load needs to be supplied with 6 V, while its resistance is 10 kΩ. To solve such a problem, it is recommended to use resistors whose resistance is ten times less than the load value, therefore, taking R 1 = 1 kΩ and substituting all known values into the formula for the voltage across the resistor, it turns out that 6 = R 2 * 12 (1000+ R 2) hence R 2 = 1 kOhm.
Now, knowing all the values, you can check the accuracy of the calculation. The drop in the potential difference across the first element is calculated as U 1 = 1000 * 12 / (1000 + 1000) = 6 V, and the total voltage - Utot = U 1+ U 2 = 12 V, which corresponds to the value of the power source.
It should be noted that the use of pull-down resistors is only used with low-power loads, since part of the energy is converted into heat, and the efficiency (efficiency) is very short.
Calculations online
With the help of programming languages (Java, Python, PHP), applications are created that allow online calculation of the required resistor parameters to remove the required voltage value from it. The scripts written by them contain all the necessary formulas and calculation algorithms. Therefore, having entered the initial data, literally in a second it will be possible to get the result.
Usually, the offered online calculators contain a graphical representation of the circuit for clarity. The suggested characteristics for input are usually:
- input voltage, V;
- undervoltage, V;
- resistance Rn, Ohm.
Please note that all values are entered in accordance with the SI.
After entering the data and pressing the "Calculate" button, in addition to directly determining the required resistance, the programs most often give out the minimum value of the required power of the elements.
Thus, it is not so difficult to calculate the voltage drop across a resistive element. To do this, you need to know the features of parallel and serial connection, as well as Ohm's law. And if there are many elements in the chain, then you can use online calculators.
